{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CR56AKRM2KBOAGZ4OC463IDCGQ","short_pith_number":"pith:CR56AKRM","canonical_record":{"source":{"id":"1208.3342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-16T11:23:28Z","cross_cats_sorted":[],"title_canon_sha256":"42d9a9b5b0664cb31e9bc63f7015384546cb879b8ceb8f39537885a08cb49191","abstract_canon_sha256":"c48fd52c5a540ea5f71070e5140a2f4cb7c5402557960c6fb99725e69d171925"},"schema_version":"1.0"},"canonical_sha256":"147be02a2cd282e01b3c70b9eda062343ad8d3f1ff31e8e4fceca24b03f06721","source":{"kind":"arxiv","id":"1208.3342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3342","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3342v1","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3342","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"pith_short_12","alias_value":"CR56AKRM2KBO","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CR56AKRM2KBOAGZ4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CR56AKRM","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CR56AKRM2KBOAGZ4OC463IDCGQ","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-16T11:23:28Z","cross_cats_sorted":[],"title_canon_sha256":"42d9a9b5b0664cb31e9bc63f7015384546cb879b8ceb8f39537885a08cb49191","abstract_canon_sha256":"c48fd52c5a540ea5f71070e5140a2f4cb7c5402557960c6fb99725e69d171925"},"schema_version":"1.0"},"canonical_sha256":"147be02a2cd282e01b3c70b9eda062343ad8d3f1ff31e8e4fceca24b03f06721","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:26.631676Z","signature_b64":"LlW17kODTWZ5BoY4Pn65fED/M6SyKnpVzjyRt5Q4YPGRMdalEtPC3YZtUNAQfGcCU2yMYiDO09x1Y4TNzhrMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"147be02a2cd282e01b3c70b9eda062343ad8d3f1ff31e8e4fceca24b03f06721","last_reissued_at":"2026-05-18T00:46:26.631077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:26.631077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3342","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Bb/Psj1RymAmrYNvv+s5ieG/e4WJvD52cc40QHQ45mG68j2+Z7Y8XNDHMcky/9xj6er+Qw3cP5P0V9uYKb9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:38:45.950987Z"},"content_sha256":"04f339e861439db14664cfc5d1c6331c40febd6f39f448b264ebb40e9a2d59aa","schema_version":"1.0","event_id":"sha256:04f339e861439db14664cfc5d1c6331c40febd6f39f448b264ebb40e9a2d59aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CR56AKRM2KBOAGZ4OC463IDCGQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Index hypergeometric integral transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yury A. Neretin","submitted_at":"2012-08-16T11:23:28Z","abstract_excerpt":"This is a brief overview of the index hypergeometric transform (other terms for this integral operator are: Olevskii transform, Jacobi transform, generalized Mehler--Fock transform). We discuss applications of this transform to special functions and harmonic analysis. The text is an addendum to the Russian edition of the book by G.E.Andrews, R.Askey, and R.Roy, Special Functions, Encycl. of Math. Appl. 71, Cambridge Univ. Press, 1999."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3342","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aq0Y+BpulucNykLOQAdBhlB/16EHYSbc4iVR2cG/K9HbZOJToUpOjpNuZ1LcwxTJKLotwhchYKM5plaq0/G3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:38:45.952186Z"},"content_sha256":"79b382b0ea3662e4f2695954f69ac7828bf33fc271660fc0c5935bab081cd854","schema_version":"1.0","event_id":"sha256:79b382b0ea3662e4f2695954f69ac7828bf33fc271660fc0c5935bab081cd854"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CR56AKRM2KBOAGZ4OC463IDCGQ/bundle.json","state_url":"https://pith.science/pith/CR56AKRM2KBOAGZ4OC463IDCGQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CR56AKRM2KBOAGZ4OC463IDCGQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T23:38:45Z","links":{"resolver":"https://pith.science/pith/CR56AKRM2KBOAGZ4OC463IDCGQ","bundle":"https://pith.science/pith/CR56AKRM2KBOAGZ4OC463IDCGQ/bundle.json","state":"https://pith.science/pith/CR56AKRM2KBOAGZ4OC463IDCGQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CR56AKRM2KBOAGZ4OC463IDCGQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CR56AKRM2KBOAGZ4OC463IDCGQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c48fd52c5a540ea5f71070e5140a2f4cb7c5402557960c6fb99725e69d171925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-16T11:23:28Z","title_canon_sha256":"42d9a9b5b0664cb31e9bc63f7015384546cb879b8ceb8f39537885a08cb49191"},"schema_version":"1.0","source":{"id":"1208.3342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3342","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3342v1","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3342","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"pith_short_12","alias_value":"CR56AKRM2KBO","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CR56AKRM2KBOAGZ4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CR56AKRM","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:79b382b0ea3662e4f2695954f69ac7828bf33fc271660fc0c5935bab081cd854","target":"graph","created_at":"2026-05-18T00:46:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This is a brief overview of the index hypergeometric transform (other terms for this integral operator are: Olevskii transform, Jacobi transform, generalized Mehler--Fock transform). We discuss applications of this transform to special functions and harmonic analysis. The text is an addendum to the Russian edition of the book by G.E.Andrews, R.Askey, and R.Roy, Special Functions, Encycl. of Math. Appl. 71, Cambridge Univ. Press, 1999.","authors_text":"Yury A. Neretin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-16T11:23:28Z","title":"Index hypergeometric integral transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3342","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:04f339e861439db14664cfc5d1c6331c40febd6f39f448b264ebb40e9a2d59aa","target":"record","created_at":"2026-05-18T00:46:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c48fd52c5a540ea5f71070e5140a2f4cb7c5402557960c6fb99725e69d171925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-16T11:23:28Z","title_canon_sha256":"42d9a9b5b0664cb31e9bc63f7015384546cb879b8ceb8f39537885a08cb49191"},"schema_version":"1.0","source":{"id":"1208.3342","kind":"arxiv","version":1}},"canonical_sha256":"147be02a2cd282e01b3c70b9eda062343ad8d3f1ff31e8e4fceca24b03f06721","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"147be02a2cd282e01b3c70b9eda062343ad8d3f1ff31e8e4fceca24b03f06721","first_computed_at":"2026-05-18T00:46:26.631077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:26.631077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LlW17kODTWZ5BoY4Pn65fED/M6SyKnpVzjyRt5Q4YPGRMdalEtPC3YZtUNAQfGcCU2yMYiDO09x1Y4TNzhrMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:26.631676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04f339e861439db14664cfc5d1c6331c40febd6f39f448b264ebb40e9a2d59aa","sha256:79b382b0ea3662e4f2695954f69ac7828bf33fc271660fc0c5935bab081cd854"],"state_sha256":"be3a054a83ba86e9c0d2f07c62861ae3919893d7d65c53a8c3aa88fb958626e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"duC+O5zuIsE6Lklf8mFAZZLgA7r4JLAkrA8lVHsXvYk4ribkd7wt5JT5AxI3W1srEc9KOaZthRmRedKQYP9jDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:38:45.956218Z","bundle_sha256":"29350168929b19c4d499e3c25495183f3fbcc936f6573f8301f3003bebaacb9e"}}